func TestSettingZeroDistanceAndExact(t *testing.T) {
expected := [][]bool{
[]bool{false, true, false, false, false, false, false},
[]bool{false, true, true, false, false, false, false},
[]bool{false, false, true, false, false, true, false},
[]bool{false, false, false, false, false, false, false},
[]bool{false, false, false, false, false, false, false},
[]bool{false, false, false, false, false, false, false},
[]bool{false, false, false, false, false, false, false}}
c, m, visited, exact, d := coupling.SetUpTest()
w := matching.FindFeasibleMatching(m, 0, 3, &c)
setpair.Setpair(m, w, exact, visited, d, &c)
nonz := findNonZero(w, exact, d, &c)
setZerosDistanceToZero(w, nonz, exact, d, &c)
for i := 0; i < len(expected); i++ {
for j := 0; j < len(expected[0]); j++ {
assert.Equal(t, expected[i][j], exact[i][j], "the cell (%v,%v) were not correcly set", i, j)
}
}
assert.True(t, utils.ApproxEqual(d[0][1], 1), "the distance for node (0,1) was changed")
assert.True(t, utils.ApproxEqual(d[2][2], 0), "the distance for node (1,1) was not set to 0")
}
func TestGuassian(t *testing.T) {
a := [][]float64{[]float64{1.0, -(1.0 / 6.0)}, []float64{0.0, 1.0}}
b := []float64{5.0 / 6.0, 1.0 / 2.0}
x, err := GaussPartial(a, b)
assert.Equal(t, nil, err, "the linear equations was not calculate correctly")
assert.True(t, utils.ApproxEqual(x[0], 11.0/12.0), "the found x value was not 11/12")
assert.True(t, utils.ApproxEqual(x[1], 0.5), "the found x value was not 1/2")
}
func TestDisc(t *testing.T) {
c, m, visited, exact, d := coupling.SetUpTest()
w := matching.FindFeasibleMatching(m, 0, 3, &c)
setpair.Setpair(m, w, exact, visited, d, &c)
Disc(1.0, w, exact, d, &c)
assert.True(t, utils.ApproxEqual(d[0][3], 0.9133), "the distance was not correctly set")
assert.True(t, utils.ApproxEqual(d[2][3], 0.49), "the distance was not correctly set")
}
func TestGoVerticalReturnsTrue(t *testing.T) {
c := setUpCoupling()
min := 0.3
n := c.Nodes[1]
done := goVertical(n, 1, 0, 1, 1, 2, 2, 2, &min)
assert.True(t, done, "goVertical did not compplete the stepping stone path")
assert.True(t, utils.ApproxEqual(0.0, n.Adj[1][0].Prob), "the cell (1 0) were changed")
assert.False(t, utils.ApproxEqual(0.3, n.Adj[1][1].Prob), "the cell (1 1) were not changed")
}
func updateEdge(edge *coupling.Edge, signal bool, min float64, n *coupling.Node) {
if signal {
log.Printf("increasing at cell (%v,%v)", edge.To.S, edge.To.T)
// increase and set the node to basic
edge.Prob += min
if !edge.Basic {
edge.Basic = true
n.BasicCount++
}
// add the main node as a successor to the node if it not already is
if !coupling.IsNodeInSlice(n, edge.To.Succ) {
edge.To.Succ = append(edge.To.Succ, n)
}
} else {
log.Printf("decreasing at cell (%v,%v)", edge.To.S, edge.To.T)
edge.Prob -= min
// if the line edge.Prob -= min, makes edge.Prob to zero, it is not a basic cell
edge.Basic = !utils.ApproxEqual(edge.Prob, 0)
// if no longer basic remove the main node as a successor for the node
if !edge.Basic {
coupling.DeleteNodeInSlice(n, &edge.To.Succ)
n.BasicCount--
}
}
edge.To.Visited = false
}
func updateNode(node *coupling.Node, newValues []float64) {
if (len(node.Adj) * len(node.Adj[0])) != len(newValues) {
log.Printf("%v %v", (len(node.Adj) * len(node.Adj[0])), len(newValues))
panic("The amount of new values does not match the adjacency matrix!")
}
k := 0
for i := range (*node).Adj {
for _, edge := range (*node).Adj[i] {
prevBasic := edge.Basic
prob := newValues[k]
if utils.ApproxEqual(prob, 0.0) {
edge.Basic = false
coupling.DeleteNodeInSlice(node, &edge.To.Succ)
if prevBasic {
node.BasicCount--
}
} else {
edge.Basic = true
if !prevBasic {
node.BasicCount++
}
if !coupling.IsNodeInSlice(node, edge.To.Succ) {
edge.To.Succ = append(edge.To.Succ, node)
}
}
edge.Prob = prob
k++
}
}
}
func TestCorrectLinearFunctionsCreated(t *testing.T) {
c, m, visited, exact, d := coupling.SetUpTest()
w := matching.FindFeasibleMatching(m, 0, 3, &c)
setpair.Setpair(m, w, exact, visited, d, &c)
a, b, index := setUpLinearEquationFrame()
setUpLinearEquations(w, exact, d, &a, &b, 0, &index, 1.0)
checkEquationDimensions(t, a, b, index, 2)
assert.True(t, utils.ApproxEqual(b[0], 0.83))
assert.True(t, utils.ApproxEqual(b[1], 0.49))
assert.Equal(t, 1.0, a[0][0], "the value in the matrix diagonal was not 1.0")
assert.True(t, utils.ApproxEqual(a[0][1], -0.17), "the value in the matrix was not -0.17")
assert.Equal(t, 0.0, a[1][0], "the value in the matrix was not 0.0")
assert.Equal(t, 1.0, a[1][1], "the value in the matrix diagonal was not 1.0")
}
func TestCorrectLinearFunctionsCreatedLoops(t *testing.T) {
c, m, visited, exact, d := coupling.SetUpTest()
w := matching.FindFeasibleMatching(m, 0, 3, &c)
setpair.Setpair(m, w, exact, visited, d, &c)
a, b, index := setUpLinearEquationFrame()
// inserting two loops into the coupling
w.Adj[0][0] = &coupling.Edge{w, 0.33, true}
w.Adj[2][2].To.Adj[1][2] = &coupling.Edge{w, 0.34, true}
setUpLinearEquations(w, exact, d, &a, &b, 0, &index, 1.0)
checkEquationDimensions(t, a, b, index, 2)
assert.True(t, utils.ApproxEqual(b[0], 0.5))
assert.True(t, utils.ApproxEqual(b[1], 0.49))
assert.True(t, utils.ApproxEqual(a[0][0], 0.67), "the value in the matrix diagonal was not 0.67")
assert.True(t, utils.ApproxEqual(a[0][1], -0.17), "the value in the matrix was not -0.17")
assert.True(t, utils.ApproxEqual(a[1][0], -0.34), "the value in the matrix was not 0.0")
assert.Equal(t, 1.0, a[1][1], "the value in the matrix diagonal was not 1.0")
}
func TestCorrectNestedMatchingFound(t *testing.T) {
expected := [][]float64{
[]float64{0.33, 0.17, 0.0},
[]float64{0.0, 0.16, 0.34}}
// the same functions used for random matching testing
c, m, visited, exact, d := coupling.SetUpTest()
w := matching.FindFeasibleMatching(m, 0, 3, &c)
Setpair(m, w, exact, visited, d, &c)
node := w.Adj[2][2].To
for i := 0; i < len(expected); i++ {
for j := 0; j < len(expected[0]); j++ {
assert.True(t, utils.ApproxEqual(expected[i][j], node.Adj[i][j].Prob), "the correct probability for cell (%v,%v) were not inserted", i, j)
}
}
}
func findDemandedPairs(w *coupling.Node, visited [][]bool) []*coupling.Edge {
demanded := make([]*coupling.Edge, 0)
for _, rows := range w.Adj {
for _, edge := range rows {
if utils.ApproxEqual(edge.Prob, 0.0) {
continue
}
if visited[edge.To.S][edge.To.T] || visited[edge.To.T][edge.To.S] {
continue
}
demanded = append(demanded, edge)
}
}
return demanded
}
func TestCorrectMatchingFound(t *testing.T) {
expected := [][]float64{
[]float64{0.33, 0.0, 0.0},
[]float64{0.0, 0.33, 0.0},
[]float64{0.0, 0.0, 0.17},
[]float64{0.0, 0.0, 0.17}}
c := coupling.New()
m := coupling.SetUpMarkov()
w := FindFeasibleMatching(m, 0, 3, &c)
for i := 0; i < len(expected); i++ {
for j := 0; j < len(expected[0]); j++ {
assert.True(t, utils.ApproxEqual(expected[i][j], w.Adj[i][j].Prob), "the correct probability were not inserted")
}
}
}
func updateUntilOptimalSolutionsFound(lambda float64, m markov.MarkovChain, node *coupling.Node, exact [][]bool, visited [][]bool, d [][]float64, c coupling.Coupling, TPSolver func(markov.MarkovChain, *coupling.Node, [][]float64, float64, int, int), solvedNodes []*coupling.Node) {
log.Printf("find optimal for: (%v,%v)", node.S, node.T)
min, i, j := uvmethod.Run(node, d)
// if min is negative, we can further improve it, so we update it using the TPSolver and iterated until we cannot improve it further
for min < 0 && !utils.ApproxEqual(min, 0) {
previ, prevj := i, j
TPSolver(m, node, d, min, i, j)
setpair.Setpair(m, node, exact, visited, d, &c)
disc.Disc(lambda, node, exact, d, &c)
min, i, j = uvmethod.Run(node, d)
if previ == i && prevj == j && min < 0 {
break
}
}
// append solved nodes such that we do not end up recurively calling nodes that have already been found to be optimal
solvedNodes = append(solvedNodes, node)
for _, row := range node.Adj {
for _, edge := range row {
if edge.To.Adj == nil {
// if the node do not have an adjacency matrix or is exact, we do not have to proccess it
continue
}
if coupling.IsNodeInSlice(edge.To, solvedNodes) {
// if the node has already been proccesses, we do not have to do it again
continue
}
updateUntilOptimalSolutionsFound(lambda, m, edge.To, exact, visited, d, c, TPSolver, solvedNodes)
}
}
exact[node.S][node.T] = true
exact[node.S][node.T] = true
return
}
func visit(root *Node, results []*Node) []*Node {
// log.Printf("%s, %s", root.S, root.T)
if root.Adj == nil {
return results
}
for i := range root.Adj {
for j := range root.Adj[0] {
edge := root.Adj[i][j]
toVisit := edge.To
if !edge.Basic || toVisit.Visited {
continue
} else if !utils.ApproxEqual(edge.Prob, 0) {
toVisit.Visited = true
results = append(results, toVisit)
results = visit(toVisit, results)
}
}
}
return results
}
func TestOptimalSolutionFound(t *testing.T) {
c, m, visited, exact, d := coupling.SetUpTest()
d = sets.InitD(len(m.Transitions))
w := matching.FindFeasibleMatching(m, 0, 3, &c)
setpair.Setpair(m, w, exact, visited, d, &c)
// the expected solution is not precice since the markov chain used do not use precise fractions
expected := [][]float64{
[]float64{0, 0.33, 0},
[]float64{0, 0, 0.33},
[]float64{0.17, 0, 0},
[]float64{0.16, 0, 0.01}}
min, i, j := uvmethod.Run(w, d)
Solve(m, w, d, min, i, j)
for i := range w.Adj {
for j := range w.Adj[0] {
assert.True(t, utils.ApproxEqual(expected[i][j], w.Adj[i][j].Prob), "the optimal probability found was not what we expected")
}
}
}
func FindFeasibleMatching(m markov.MarkovChain, u int, v int, c *coupling.Coupling) *coupling.Node {
n := len(m.Transitions[u])
u, v = utils.GetMinMax(u, v)
// tries to find the node (u,v) in c, if not make a new one and add to c
node := coupling.FindNode(u, v, c)
if node == nil {
node = &coupling.Node{S: u, T: v, Succ: []*coupling.Node{}}
c.Nodes = append(c.Nodes, node)
}
log.Printf("copy the transitions from the states %v and %v", u, v)
uTransitions := make([]float64, n, n)
vTransitions := make([]float64, n, n)
// copies the transitions of u and v such that we do not makes changes in the markov chain
copy(uTransitions, m.Transitions[u])
copy(vTransitions, m.Transitions[v])
// finds the length of the rows and columns in the matching for u and v
lenrow, lencol := matchingDimensions(uTransitions, vTransitions, n)
log.Printf("row and column length are: %v and %v", lenrow, lencol)
rowindex := make([]int, lenrow, lenrow)
colindex := make([]int, lencol, lencol)
// finds the row and column indexs for the u and v matching
setMatchingIndexes(uTransitions, vTransitions, n, rowindex, colindex)
log.Printf("row index: %s", rowindex)
log.Printf("column index: %s", colindex)
matching := make([][]*coupling.Edge, lenrow, lenrow)
for i := range matching {
matching[i] = make([]*coupling.Edge, lencol, lencol)
}
// fills out the matching with node pointers, using nodes already in the coupling c if they exist
filloutAdj(rowindex, colindex, lenrow, lencol, matching, c)
// completes the matching by inserting probabilities and setting appropriate cells to basic
i, j := 0, 0
for i < lenrow && j < lencol {
if utils.ApproxEqual(uTransitions[rowindex[i]], vTransitions[colindex[j]]) {
matching[i][j].Prob = uTransitions[rowindex[i]]
// check if we are in the lower right corner, such that we do not get an out of bounds error
if !(i+1 == lenrow && j+1 == lencol) {
matching[i][j+1].Basic = true
node.BasicCount++
}
matching[i][j].Basic = true
matching[i][j].To.Succ = append(matching[i][j].To.Succ, node)
node.BasicCount++
i++
j++
} else if uTransitions[rowindex[i]] < vTransitions[colindex[j]] {
matching[i][j].Prob = uTransitions[rowindex[i]]
vTransitions[colindex[j]] = vTransitions[colindex[j]] - uTransitions[rowindex[i]]
matching[i][j].Basic = true
matching[i][j].To.Succ = append(matching[i][j].To.Succ, node)
node.BasicCount++
i++
} else {
matching[i][j].Prob = vTransitions[colindex[j]]
uTransitions[rowindex[i]] = uTransitions[rowindex[i]] - vTransitions[colindex[j]]
matching[i][j].Basic = true
matching[i][j].To.Succ = append(matching[i][j].To.Succ, node)
node.BasicCount++
j++
}
}
log.Println("Logging matching:")
for i := 0; i < lenrow; i++ {
for j := 0; j < lencol; j++ {
log.Printf(" - At: u %d, %d prob: %f, basic: %t",
matching[i][j].To.S,
matching[i][j].To.T,
matching[i][j].Prob,
matching[i][j].Basic)
}
}
node.Adj = matching
return node
}
